Rechargeable aluminum ion batteries (AIBs) with low cost and nonflammability have attracted considerable interest for electronics and grid energy storage, however, developing densely-compact cathodes, with rapid ion/electron transport channels and high energy storage capability remains challenging. Herein, we reported the facile construction of the nanoporous densely-stacked films derived from three-dimensional (3D) graphene aerogels, prepared by the self-propagating combustion rapid reduction of graphene oxide aerogels within seconds, as advanced binder-free cathode for ultrafast and high-capacity AIBs. Owing to the notable characteristics of 3D interconnected yet nanoporous structure, large surface area (513 m2 g-1), high electrical conductivity (581 S cm-1), dense stacking (0.61 g cm-3), expanded interlayer spacing (3.69 Å) of graphene aerogel-derived compact film, the as-assembled AIBs deliver considerably high capacity of 245 mAh g-1 at 1 A g-1, at least twice of graphite for AIBs. Impressively, our AIBs display exceptional rate capability, showing 70 mAh g-1 at a high current density of 15 A g-1, coupled with superstable cycling stability without obvious capacity decay after 5000 times, and wide temperature operation from 0 to 60 oC, outperforming most reported carbon based cathodes for AIBs.